This isn't about some fundamental East/West attitude difference. From time immemorial it was like that in the West too, the change came with the late 19th century and mainly the 20th century when government took on the role of caretaker with pensions, welfare and various government transfers, reducing interpersonal dependencies, and allowing more atomized lifestyles.
I don’t see it as a big government intervention that drove the change. I think it was a big change in housing availability and the suburbs. This was driven by WW2 victory and the industrial production machine. Making housing affordable available to small families.
The same thing happened also in Europe which didn't have that type of suburbia, nor necessarily that sort of WW2 win. These social changes were a slow ramp, not some single event changing things. It was in part technology, in part state centralization capacity via administration development, in part ideologies and philosophies etc. Both socialism and capitalism pushed against traditional kin and clan structures in favor of universal platforms (markets, or universal co-ownership). But already the Church laid some of the foundations of all this. And then the church also weakened as a slow erosion and social norms were markedly more liberal in e.g. the 19th century than in the 18th and so on.
Europe had the weird circumstances of being destroyed both families and buildings after WW2. They also experienced the Marshall plan of rebuilding. No doubt there is no simple answer to how we got here. The move from agrarian society to industrial society also had an effect. I just have a hard time applying a motivation to a government. I can see it as a by product.
